Simplify the expression. $(z^{3}-4z)(-5z^{4}+z^{3}+6z)$
Explanation: First use the distributive property. $ z^3 (-5 z^4) + z^3 ( z^3) + z^3 (6 z) - 4 z (-5 z^4) - 4 z ( z^3) - 4 z (6 z) $ Simplify. $ - 5z^{7} + 1z^{6} + 6z^{4} + 20z^{5} - 4z^{4} - 24z^{2} $ $-5z^{7}+z^{6}+20z^{5}+2z^{4}-24z^{2}$ Identify like terms. $ {- 5z^{7}} {+ 1z^{6}} {+ 6z^{4}} {+ 20z^{5}} {- 4z^{4}} {- 24z^{2}} $ Add the coefficients. $ { -5z^{7}} {+ z^{6}} {+ 20z^{5}} {+ 2z^{4}} { -24z^{2}} $